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Designing and Implementing Nervous System Simulations on LEGO Robots

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Published on: May 25, 2013

Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations.

Michael Hopkins¹, Mantas Mikaitis¹, Dave R Lester¹

¹APT research group, Department of Computer Science, The University of Manchester, Manchester, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|January 21, 2020

Summary

Stochastic rounding with fixed-point arithmetic improves accuracy for solving ordinary differential equations (ODEs), offering a more energy-efficient alternative to standard methods. This approach enhances computational neuroscience and other scientific fields.

Keywords:

Izhikevich neuron model SpiNNaker dither fixed-point arithmetic ordinary differential equation stochastic rounding

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Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

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Published on: March 2, 2015

Area of Science:

Computational neuroscience
Numerical analysis
High-performance computing

Background:

Double-precision floating-point arithmetic is standard in high-performance computing but demands significant energy and memory.
Reduced-precision arithmetic offers potential gains in efficiency but often introduces numerical errors.
Accurate numerical solutions are critical in fields like neuroscience for modeling complex systems.

Purpose of the Study:

To investigate methods for enhancing the accuracy of reduced-precision fixed-point arithmetic.
To evaluate these methods in the context of solving ordinary differential equations (ODEs) for neuroscience applications.
To explore computationally cheaper alternatives inspired by digital signal processing techniques.

Main Methods:

Utilizing the Izhikevich neuron model to simulate neuronal behavior and test ODE solvers.
Comparing fixed-point arithmetic with stochastic rounding against single-precision floating-point and round-to-nearest fixed-point methods.
Investigating a dither-inspired technique for improved resolution in fixed-point arithmetic.

Main Results:

Fixed-point arithmetic with stochastic rounding demonstrated superior accuracy in spike timing compared to single-precision floating-point and round-to-nearest fixed-point arithmetic.
The observed improvements held across various neuron behaviors and ordinary differential equation solvers.
A computationally inexpensive dither-based method also showed promise for enhancing accuracy.

Conclusions:

Stochastic rounding is a key factor in achieving accurate results with reduced-precision fixed-point arithmetic for ODE solutions.
These findings have broad implications for solving ODEs in neuroscience and other scientific domains, including those involving partial differential equations.
Reduced-precision arithmetic, when carefully implemented, can provide an energy-efficient and accurate alternative for scientific computation.